The p-value of the test is 0.1515 which concludes that the average amount of arsenic in chicken from suppliers is 80 ppb.
The test hypothesis is as follows:
H₀: The mean amount of arsenic is 80 ppb, i.e. μ= 80.
Hₐ: The mean amount of arsenic is more significant than 80 ppb, i.e.μ > 80.
We will apply a t-test for a single mean because the population standard deviation is unknown,
It is assumed that the sample means [tex]\bar{x}[/tex] = 91.
The adjusted sample presented is:
S = { 62, 78, 89, 95, 95, 137}
Calculate the sample standard deviation as follows:
[tex]\bar{x}[/tex] = 62 + 78 + 89 + 95 + 95 + 137 =80
[tex]s =\sqrt{\frac{1}{6-1} \times [(62-80)^2 + (78-80)^2 + (89-80)^2 + (95-80)^2 + (95-80)^2 + (137-80)^2]}[/tex]
s =28.66
[tex]t =\dfrac{\bar{x}-\mu}{s/ \sqrt{n} } = \dfrac{{91}-80}{28.6/ \sqrt{6} }=0.94[/tex]
Thus, the test statistic value is 0.94.
Compute the p-value of the test as follows:
p-value = p(tₙ₋₁ < t)
p-value = p(t₆₋₁ < t)
p-value = p(t₅ < t)
*Make use of a t-table.
As a result, the test has a p-value of 0.1515.
Rule of decision:
The null hypothesis will be rejected if the p-value of the test is less than the significance threshold, and vice versa.
p-value = 0.1515 > α = 0.05
At 5% significance, the null hypothesis will not be rejected.
As a result, we may conclude that the average amount of arsenic in chicken from suppliers is 80 ppb.
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Expand and state your answer as a polynomial in standard form. (4x³+y³)²
Answer:
16x⁶+y⁶
Step-by-step explanation:
(4x^3+y^3) (4x^3+y^3)
= 16x^6+y^6
Find the measure of angles 1 and 2
Answer:
both angles 1 and 2 measure 135°
Step-by-step explanation:
angle 1 = angle 2 = 135°
Hope this helps
a sample of experienced typists revealed that their mean typing speed is 95 words per minute and the median typing speed is 77 words per minute. the standard deviation of typing speed is 16.9 words per minute. what is the pearson's coefficient of skewness?
The pearson's coefficient of skewness is found as the 1.065.
What is termed as the coefficient of skewness?The coefficient of skewness is a measurement used to evaluate the strength and direction of skewness in a sample distribution using descriptive statistics such as mean, median, or mode. The skewness coefficient is used to compare a distribution of the sample to a normal distribution.Pearson skewness:
The skewness of the a data set is calculated by subtracting the mean from the median and dividing by the standard deviation.
In this case:
The mean is 95, the median is 77, as well as the standard deviation is 16.9. So,
Pearson skewness = (95 - 77)/16.9
Pearson skewness = 1.065.
Thus, the pearson's coefficient of skewness is found as the 1.065.
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Write an equation that represents the line.
Use exact numbers.
The equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph:
The two points are:
(0, -3) and (1, -5)
The equation of the line:
y - (-5) = [-5 - (-3)]/[1] (x - 1)
y + 5 = -2(x - 1)
y = -2x -3
Thus, the equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).
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What is an equation of the line that passes through the point (1,−7)
(1,−7) and is parallel to the line 3x+y=3
3x+y=3?
Answer:
[tex]3x + y = 3 \\ 3 = x - y \\ 3 = x[/tex]
Answer:
y = -3x - 4
Step-by-step explanation:
Pre-SolvingWe are given the equation 3x + y = 3, and we want to find an equation of the line that is parallel to 3x + y = 3.
This same line also passes through the point (1, -7).
Parallel lines have the same slopes. This means that we'll first need to find the slope of 3x + y = 3.
The equation is written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0. a is usually non-negative as well.
There is a shortcut into finding the slope when the equation is in standard form; the slope of the line is -a/b, where a is the coefficient in front of x and b is the coefficient in front of y).
The coefficient in front of x is 3, and 1 in front of y.
SolvingSubstitute 3 as a, and 1 as b in -a/b. Don't forget about the - in front of a!
-3/1 = -3
This means the slope of the line is -3.
It is also the slope of the line parallel to it.
We can write the equation of the line we are trying to solve for in standard form, too. However, we could also write it in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept.
As we are already given the slope, we can immediately plug that into the formula.
Replace m with -3.
y = -3x + b
Now we need to find b.
As the equation passes through the point (1, -7), we can use its values to help solve for b.
Substitute 1 as x and -7 as y.
-7 = -3(1) + b
Multiply.
-7 = -3 + b
Add -3 to both sides
-4 = b
Substitute -4 as b into the equation
y = -3x - 4
74. The product of a nonzero integer and 12 has the same value as the product of 3 and the square of the integer. What is the integer?
E. 2
F. 3
G. 4
H. 6
10. Rotate 90° clockwise about the origin.
a. J '(-3,-4), K'(-6,-4), L'(-4,-3), M'(-1, -3)
b. J'(-4,-3), K'(-4,-6), L'(-3,-4), M'(-3,-1)
c. J'(-4, 3), K'(-4, 6), L'(-3, 4), M'(-3, 1)
d. J'(4, -3), K'(4, -6), L'(3,-4), M'(3,-1)
Check the picture below.
How many 1/4 inch pieces can be cut from a piece of ribbon 9/20 of an inch long
Something Is DIFFERENT about this problem..
I'm not sure what..
991 + 2 = ?
Answer: 993
Step-by-step explanation:
I BELIEVE THE ANSWER IS 993 BUT I'M NOT SURE !
It could be 10,000 i don't know but i'm pretty sure it's 993 !
Hope it helped !
Find b for the given line.
y = 3x + b; (2, 7)
The value of b for the given line is 1
What is equation of line ?The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.
Given that : y = 3x + b; (2, 7)
y =3x + b
7 = 6 + b
1 = b
The value of b for the given line is 1
The line's equation is a linear equation of degree one.
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hurry plssssssssssssss
Answer:
So the answer would be
D
Step-by-step explanation:
Use the formula an=a1rn−1 to identify the geometric sequence an=81⋅2n−13n−1
I think this is right but I'm not 100% sure
I'm like 75% sure sorry
Jina made $207 for 9 hours of work.
At the same rate, how much would she make for 13 hours of work?
Answer:
$299
Step-by-step explanation:
[tex](\frac{207}{9} )(13)=\frac{2691}{9}}} =299[/tex]
Hope this helps
Find the slope between these two points:
(-19, 12), (-9, 1)
Answer:
3.1
Step-by-step explanation:
XY is formed by X(-9,-7) and Y (-3,5 is line j is the perpendicular bisector of XY
The Equation of perpendicular bisector line l is found to be [tex]y = 2x+ 11[/tex]
Given Line XY is formed by points X(-9, -7) and Y(-3,5) therefore, it passes through these two respective points.
Let the slope of this line be n
The Slope of line passing through X and Y points is given by
n = [tex](y_{2} - y_{1} )/(x_{2} -x_{1} )[/tex]
⇒ n = {5 - (-7) }/ {(-3) - |(-9)}
⇒ n = 12/6
⇒ n = 2 (equation 1 )
Given that line l is perpendicular bisector of XY
Let the slope of l = m
We know that the product of the slopes of any two perpendicular lines is -1
Therefore, n x m = -1
⇒ m = -1 \ n
putting the value of n from the above equation 1 we get
⇒ m = - 1/2
Additionally, because l is the perpendicular bisector hence it goes through the mid point of the line XY
Mid point of two lines = [tex](x_{2} + x_{1} )/2[/tex] and [tex](y_{2} + y_{1} )/2[/tex]
Mid point of XY = [tex]\frac{-9 + (-3)}{2}[/tex] and [tex]\frac{-7 + (5)}{2}[/tex]
= (-6, -1)
The equation of perpendicular bisector l is given my the following formula:
[tex]y = nx + c[/tex]
here we have n = slope of line
we have n = 2 from equation 1
∴ y = 2x + c (equation 2)
Also equation (2) is satisfied by the point (-6,-1)
Hence we can express it as:
-1 = 2(-6) + c
⇒ c = 11
Therefore the required equation of perpendicular bisector l is
[tex]y = 2x + 11[/tex]
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sheriff dale and sheriff john left the station at the same time in response to calls. dale drove north, john drove west, and dale drove at an average speed of 20mph faster than john. after 30 minutes, they were exactly 50 miles apart. what was john's average driving speed?
John's driving at a speed of 40 miles per hour
Given that,
Dale and John leave their home traveling in different directions on a straight road. Dale drives 20 miles per hour faster than John. After 30 minutes they are 50 miles apart.
a. Define a variable for Dale's rate: x mph
Write an expression for John's rate: x-20 mph
-------
b. Write and solve an equation to find Dale rate. Then find John's rate.
They are separating at the rate of x + x-20 = 2x-20 mph.
-------
Equation:
time*speed = distance
0.5(2x-20) = 50 miles
x-10 = 50
x = 60 miles
x = 60
----
John's rate = x-20 = 40 mph
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Worth 19 points, pls help
Evaluate. Write your answer as a whole number or as a simplified fraction.
3-1.9-¹ =
Answer:
27^-1
Step-by-step explanation:
1/3 ×1/9=1/27=27^-1
Ellie is six years older than Maisie Zoe is twice as old as Eli. The sum of their ages is 50. How old is Zoe?
Let the age of Maisie be x
From the first statement, Ellie is six years older than Maisie implying:
[tex]\text{Ellie's age = x + 6}[/tex]From the second statement, Zoe is twice as old as Eli implying:
[tex]\text{Zoe's age = 2(x+6)}[/tex]From the last statement, the sum of their ages is 50 implying:
[tex]x\text{ + x + 6 + }2(x\text{ + 6) = 50}[/tex]Solving for x:
We open the bracket and collect like terms
[tex]\begin{gathered} x+x\text{ + }6\text{ + 2x + 12 = 50} \\ x\text{ + x + 2x + 6 + 12 = 50} \\ 4x\text{ + 18 = 50} \\ 4x\text{ = 50 - 18} \\ 4x\text{ = 32 } \\ \text{Divide both sides by 4} \\ \frac{4x}{4}\text{ = }\frac{32}{4} \\ x\text{ = 8} \end{gathered}[/tex]Hence, Zoe's age is:
[tex]\begin{gathered} =2(x\text{ + 6)} \\ =\text{ 2(8+6)} \\ =\text{ 2 }\times\text{ 14} \\ =\text{ 28} \end{gathered}[/tex]Answer:
Zoe's age = 28
One triangle in the diagram below can be mapped onto the other using two reflections. Identify the
lines of reflection that would map one onto the other. Can you map one triangle onto the other using
just one basic rigid motion? If so, explain.
look at photo MATHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
The fraction is 47/200. The decimal is 0.235.
A percentage can be written in a fraction form by putting 100 on the denominator. For example, the fraction corresponding to x % is x/100.
For converting a percentage into a decimal first it should be converted into fractions as fractions can only be converted into decimal.
For example, the decimal for the fraction 50% is 0.5, which is given by writing 50% as 50/100 = 0.5 after putting decimal on 2 places left to 50.
So here the given percentage is 23.5%.
The corresponding fraction is 23.5/100 = 235/1000 = 47/200 after eliminating the decimal on the numerator and simplifying.
Now the corresponding decimal is, 0.235. Since 1000 is in the denominator for 235/1000, we can simply find the decimal by putting decimal point on 3 places left to 235.
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Please help
It’s due tonight
Answer: 21
Step-by-step explanation:
11,000 with a 5/10/25 chain discount. Calculate the net price and trade discount
After the discount the net price is $7053.75 and the trade discount is 35.875% .
The term discount designates a sum or a percentage subtracted from an item's usual selling price.
A discount is a decrease in the cost of a commodity or service. Chain discounts can also be applied using the complement approach. To calculate each discount's complement, first subtract the discount from 100%. The net-price rate can be calculated by multiplying the complements to find the percentage that you really pay. The dollar value of the discount can also be determined using the complement technique.The given marked price of the article is 11000
Price after first discount of 5% = 11000 - 5% of 11000 = 10450
Price after second discount of 10% = 10450 - 10% of 10450 = 9405
Price after third discount of 25% = 9405 - 25% of 9405 = 7053.75
Therefore the net price is 7053.75.
Therefore the trade discount is = ( 11000 - 7053.75 ) ÷ 11000 = 0.35875
Trade discount percentage = 35.875%
Hence after the discount the net price is $7053.75 and the trade discount is 35.875% .
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A trader is given 15% discount on goods bought from a factory. If the original price of the item bought from the factory is ¢45000000, calculate I. The discount on the item.
II. The amount the trader paid for item
If a trader is given a 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, then
(I) The discount amount will be ¢6750000
(II) The final amount that the trader will have to pay to buy the goods will be ¢38250000.
As per the question statement, a trader is given 15 Percent discount on goods bought from a factory and the original price of the item bought from the factory is ¢45000000.
We are required to calculate the discount amount, and the final amount that the trader will have to pay to buy the goods.
To solve this question, we simply need to calculate 15 percent of 45000000, and then subtract the calculated discount amount from ¢45000000.
Therefore, 15 percent of ¢45000000 = ¢[(15/100) * 45000000]
= ¢(15 * 450000)
= ¢6750000
That is, on 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, the discount amount is ¢6750000.
And, considering the discount of ¢6750000 on the factory price of ¢45000000, the final amount that the trader will have to pay to buy the goods = ¢(45000000 - 6750000)
= ¢38250000.
Percent: In mathematics, a percentage is a number or a ratio expressed as a fraction with 100 as the denominator, and is often denoted using the percent sign, "%".Discount: In Mathematics and basic accountancy, a Discount is an amount of rebate which is subtracted from the selling price of an item, and the customer can pay that rebated price to own the item.To learn more about percents and discounts, click on the link below.
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2x+3y=5x−y
Complete the missing value in the solution to the equation
( ,0)
Answer:dsafdf
Step-by-step explanation's
A store sells 12 cans of fruitcocktail for $21.How much would it cost you to buy 7 cans of fruit cocktail?
Answer:
$189
Step-by-step explanation:
you would take 27 × 7 and multiply the two numbers, then get your answer.
Answer:
$12.25
Step-by-step explanation:
The unit rate would be[tex]\frac{21}{12}[/tex] 1.75 a can
7 x 1.75 = 12.25
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!
Answer:
A is not equivalent
Step-by-step explanation:
A is .15 while all the others are .75 in some way
Answer:
0.15
Step-by-step explanation:trust me
y=-2
4x-3y=18
explanation needed
Answer:-2
Step-by-step explanation: Substitute the given y-value into 4x−3y=18 and solve for x
The water level in a tank measures 15 inches and is decreasing 0.5 inches every minute. How many minutes, x, will it take for the water level to measure 9 inches deep?
12 minutes .
The tank takes 12 minute for the water level to measure 9 inches deep.
Explain two step problem?A two-step problem is a word problem that must be solved in two steps.While many of these problems have only one step, a two-step word problem necessitates the solution of two different equations. Two different operations (such as multiplication and addition) or two of the same operation may be used in the two-step word problem (like subtraction and subtraction).Given tank measurement = 15 inches .
it decreases 0.5 inches every minute.
We have to the minute at which water level reaches 9 inches deep,
Here the difference of inches is 6 inches .
15 inches - 6 inches = 9 inches
To find minute ,
6 / 0.5 = 12 minute .
The tank takes 12 minute to measure 9 inches deep.
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the points (-5,r) and (2,13) lie on a with slope 3 find the missing coordinate r
Answer:
r = - 8
Step-by-step explanation:
calculate the slope m using the slope formula , then equate to 3
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, r ) and (x₂, y₂ ) = (2, 13 )
m = [tex]\frac{13-r}{2-(-5)}[/tex] = [tex]\frac{13-r}{2+5}[/tex] = [tex]\frac{13-r}{7}[/tex]
then equating gives
[tex]\frac{13-r}{7}[/tex] = 3 ( multiply both sides by 7 )
13 - r = 21 ( subtract 13 from both sides )
- r = 8 ( multiply both sides by - 1 )
r = - 8
find the 7th term 18,6,2…
If we look at the series, one third of the current term gives the numerical value of the next term.
If we need to express it algebraically, we can write the following equation.
[tex]a_{n+1}=\frac{a_{n}}{3}[/tex]Therefore, our common multiplier can be found as follows. Because this sequence is a geometric sequence.
[tex]\frac{a_{n+1}}{a_{n}} =r=\frac{1}{3}[/tex]In geometric sequences, any term can be written in terms of the first term. Below is an example.
[tex]a_{n}=a_{1}.r^{n-1}[/tex]Since we know the numerical values of the first term and the common factor of the series, we can easily find the seventh term.
[tex]a_{7}=a_{1}.r^{7-1}[/tex][tex]a_{7}=18.(\frac{1}{3} )^6[/tex][tex]a_{7}=\frac{2}{81}[/tex]